Phase noise compensation for MIMO WLAN systems

ABSTRACT

The present invention provides a method for reducing phase noise in OFDM systems by analyzing a time-dependent representation of the phase noise that changes in real time according to received data. The analysis of real time signals is based on processing statistical properties of phase noise and received data. The statistical properties of phase noise are represented by a covariance matrix R ψψ . The basis of the multiplicative phase noise decomposition which represents the varying in time phase noise component, is selected from the eigenvectors of R ψψ . The present invention suggests replacing the fixed representation of the phase noise as suggested by prior art with a system and time-dependent representation that changes in real time according to received data. 
     The method according to the present invention is implemented within An OFDM transceiver.

FIELD OF THE INVENTION

The present invention relates to wireless communications. Moreparticularly it relates to a method of compensating for carrier phasenoise in OFDM communication systems.

BACKGROUND OF THE INVENTION

Frequency division multiplexing (FDM) is a technology for transmittingmultiple signals simultaneously over a single transmission path, such asa cable or wireless system. Each signal is transmitted within its ownunique frequency range on a carrier wave that is modulated by data(text, voice, video, etc.).

The orthogonal FDM (OFDM) modulation technique distributes the data overa large number of carriers that are spaced apart at precise frequencies.This spacing provides “orthogonality”, which prevents the demodulatorsfrom detecting frequencies other than their own.

Orthogonal frequency division multiplexing (OFDM) has been implementedin the wireless local-area-network (WLAN) IEEE 802.11 as well as digitalaudio broadcasting (DAB) and asymmetric digital subscriber line (ADSL)standards.

The main advantages of OFDM are its high spectral efficiency and itsability to deal with frequency-selective fading and narrowbandinterference. The spectral efficiency of OFDM systems can be furtherincreased by adding multiple antenna techniques, also known asmultiple-input multiple-output (MIMO) techniques. The indoor deploymentof WLANs makes MIMO OFDM a strong candidate for high throughputextensions of current WLAN standards because the throughput enhancementof MIMO is especially high in richly-scattered scenarios, of whichindoor environments are typical examples.

The performance of OFDM systems is seriously affected by phase noise.Phase noise occurs due to the instability of the system localoscillator. This instability spreads the power spectral density (PSD) ofthe local oscillator across adjacent frequencies, rather than remainingconcentrated at a particular frequency. This type of phase noise iscommon in conventional oscillators. Consequently, carriers generated bythese oscillators are not strictly “orthogonal”, and thereforeinter-carrier interference (ICI) and inter-symbol interference (ISI)occurs in the received signal.

Such phase noise resulting from a difference between the carrierfrequency and the local oscillator is a limiting factor for OFDM systemperformance, particularly for high data rates. Phase noise can be seenas consisting of two components: a common phase error (CPE) componentthat is common to all carriers and a time varying component that isfrequency dependent. The time varying component, which is typicallyweaker than the CPE component, generates ICI. CPE can be removed byaveraging over all carriers. Methods for eliminating CPE are known tothose skilled in the art, e.g., a technique proposed by Schenk et al.Further improvements in phase noise suppression are disclosed in U.S.patent application no. 2004/0190637 by Maltsev, et al. They combinepilot subcarriers of data symbols to generate an observation vector.After that, recursive filtering of the observation vectors is performedto generate the phase compensation estimate. Although the generation ofobservation vectors is based on received data, the found vector isconstant during symbol time and therefore accounts only for common phasenoise. Furthermore the compensation is done in the frequency domain andtherefore cannot restore orthogonality when ICI is present.

There remains to be found a satisfactory method for suppressing ICI inOFDM systems. A common approach for ICI mitigation was presented by Wuand Bar-Ness. Another approach is time domain processing as described byCasas, et al. Casas proposes phase noise representation in a fixed basisindependent of the system or specific external conditions. The dominantphase noise components are then estimated using least square (LS)fitting of several base vectors. When single base vector is used, themethod reduces to that of Wu and Bar-Ness.

The method proposed by Casas is not an optimal solution because phasenoise cannot be compactly represented in a fixed basis for all systems.

The present patent discloses a method where phase noise is representedin a system-dependent basis (derived from the received data orprecalibrated) rather than in a fixed basis as in the prior art. Thistechnique provides a significant reduction in phase noise and works wellfor strong phase noise. The system-dependent and time-dependent basisfor phase noise representation that is proposed in the present patent isits primary innovation over previous methods. The present patent alsodiscloses other possible enhancements of the technique for MIMO systems,such as online calibration and exploitation of null tones.

SUMMARY OF THE INVENTION

The present invention relates to a method of compensating for carrierphase noise in OFDM communication systems. Phase noise occurs due to theinstability of the local system oscillator and causes inter-carrierinterference (ICI) of adjacent tones. Phase noise can be seen asconsisting of two components: a common phase error (CPE) component thatis common to all carriers and a time varying component that is frequencydependent. CPE can be removed by averaging over all carriers. Methodsfor eliminating CPE are known to those skilled in the art. The presentpatent discloses a method for reducing the time varying component ofphase noise. This method is an enhancement of the technique known in theprior art based on phase noise representation in a fixed basisindependent of the system or specific external conditions [Casas etal.]. The method proposed by Casas is not an optimal solution becausephase noise cannot be compactly represented in a fixed basis for allsystems. In the method disclosed in the present patent the phase noiseis represented in a system-dependent basis (derived from the receiveddata or pre-calibrated) rather than in a fixed basis as in the priorart. This technique provides a significant reduction in phase noise andworks well for strong phase noise. The system and time-dependent basisfor phase noise representation that is proposed in the present patent isits primary innovation over previous methods. The present patent alsodiscloses other possible enhancements of the technique for MIMO systems,such as online calibration and exploitation of null tones.

BRIEF DESCRIPTION OF THE DRAWINGS

Reference is now made to the accompanying figures, which illustrateaspects of the present invention as described above.

FIG. 1 illustrates a method of phase noise coefficient estimation. Thephase noise can be decomposed in some basis v₀, . . . , v_(N-1) withcoefficients γ=[γ₀, . . . , γ_(N-1)]^(T) (eq. 15). The d leadingcoefficients are calculated by a least squares (LS) procedure

FIG. 2 shows schematically the phase noise compensation process (eq.7-14). The coefficients {circumflex over (γ)} and basis vectors v₀, . .. , v_(d-1) of the phase noise decomposition are multiplied respectivelyand then summed over (Σ) to get e^(−j{circumflex over (φ)}) ^(i) . Themultiplicative noise e^(−j{circumflex over (φ)}) ^(i) is then removedfrom received OFDM signal z_(i).

FIG. 3 depicts calibration-based basis estimation. The figure depicts achoice of the basis elements of the phase noise decomposition from thestatistical properties of the phase noise itself.

In FIG. 4, a decision-directed basis estimation is presented. Thisenhances the proposed method of FIG. 3 by allowing the basis itself toadapt to environmental changes.

FIG. 5 illustrates an independent tracking of coefficients {circumflexover (γ)} of the multiplicative phase noise expansione^(−j{circumflex over (φ)}) ^(i) . For each i the previous values of{circumflex over (γ)}_(i) are fed into a finite impulse response (FIR)filter with coefficients β_(i1), . . . , β_(iL) then {circumflex over(γ)}_(i) is smoothed on the basis of coefficients β_(i1), . . . ,β_(iL).

FIG. 6 shows schematically joint tracking of coefficients γ=[γ₀, . . . ,γ_(d-1)]^(T) with the use of a matrix finite impulse response filter(FIR).

FIGS. 7 to 17 present experimental results from a simulation of thetechnique for phase noise reduction disclosed in the present invention.The simulation tested the technique's performance on measured WLANchannels, as well as measured phase noise.

FIG. 18 is a block diagram of the Receiver structure for SISO inaccordance with the present invention.

FIG. 19 is a block diagram of Phase noise compensation unit inaccordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

One of the main problems of OFDM systems is interference of adjacenttone signals, referred to as inter-carrier interference (ICI).

One major cause of ICI is phase noise caused by instability of localoscillators. ICI limits the use of the entire available spectrum andtherefore is a serious obstacle to increasing the system's performanceand data transfer rate.

The present invention discloses enhancements to the method of Casas, etal for reducing phase noise in OFDM systems. The Casas method is basedon representing the phase noise in a fixed basis unrelated to thespecific system, namely the transceiver specifications and environmentalparameters. The dominant phase noise components are then estimated usingLS fitting of several basis vectors. The present invention suggestsreplacing the fixed representation of the phase noise with a system andtime-dependent representation that changes in real time according toreceived data. The time-dependent representation of phase noise iscalculated on the basis of statistical properties of the phase noise,namely the phase noise time covariance. This covariance can be presentedin terms of a covariance matrix. This matrix and the LS fitting are usedto calculate the time-dependent representation of the phase noise usingbasis elements that best represent the phase noise process. Thisenhanced calculation can substantially reduce phase noise in an OFDMsystem.

To further improve the present invention, several enhancements aresuggested to the main embodiment. These enhancements can contributesubstantially to the performance of the proposed scheme by increasingthe number of available equations or improving the basis representationof the phase noise.

The first enhancement uses null tones for channel estimation rather thanjust using tones in which energy has been transmitted. The contributionof null tones depends on the amount of adjacent-channel suppression.With the appropriate amount of adjacent-channel suppression, the nulltones can be used to better estimate the level of ICI.

A further enhancement of the present invention can be achieved byapplying the proposed method to MIMO OFDM systems. In this kind ofsystem, all the transceivers use the same local oscillator. Because ofthis, phase noise can be jointly estimated from the pilot symbolsreceived by different antennas. The use of this extra informationsubstantially enhances the applicability of the proposed method andimproves the quality of the LS fitting of the coefficients.

Another significant enhancement of the present invention concerns theevaluation of the covariance matrix R_(ψψ) defined later in thisspecification. There are several ways of obtaining the covariancematrix. One way proposed in this invention is to pre-calibrate R_(ψψ)and generate basis vectors that are either measured or are calculatedfrom the local oscillator design. These options are simple to implementand are already an improvement over the use of a fixed basis, but mightlead to performance degradation due to varying environmental factorssuch as temperature or due to vendor-dependent behavior. Therefore, inaccordance with the present invention, it is further suggested thatR_(ψψ) can be estimated from received time dependent data and aneigendecomposition be applied to R_(ψψ) in order to obtain the basisvectors.

The formal mathematical description of the proposed method is given asfollows.

An OFDM system can be described by

$\begin{matrix}\begin{matrix}{{x(t)} = {\sum\limits_{k = 0}^{N - 1}{{s(k)}\;{\mathbb{e}}^{j\;\omega_{k}t}}}} & \; & {0 \leq t \leq T_{s}}\end{matrix} & (1)\end{matrix}$

where ω_(k)=ω₀+kΔω is the frequency of the k'th channel,

${k = {- \frac{N}{2}}},\ldots\mspace{14mu},\frac{N}{2},\omega_{0}$is the carrier frequency

$\begin{matrix}{{\Delta\;\omega} = \frac{2\;\pi}{T_{s}}} & (2)\end{matrix}$

is the angular sampling frequency, s(k) is the symbol transmitted by thek'th channel and is independent of symbols transmitted over otherchannels. The OFDM symbol passes through a time invariant channel (aquasi-stationary fading process is assumed) and the received signal y(t)is given byy(t)=h*x(t)+n(t)  (3)

The multiplicative phase noise results from the jitter of the localoscillator of the OFDM system. The additive Gaussian noise isrepresented by n(t) and can is treated by methods known in the priorart. In this model of the OFDM system, the received signal affected bythe phase noise can be written asz(t)=)y(t)e ^(jφ(t)) +n(t)  (4)

where φ(t) is a random process that can be considered as a filteredGaussian process with PSD P_(φ)(f). The multiplicative part of thisequation represents the varying in time phase noise component and a timedepended component. This multiplicative process ψ(l)=e^(iφ(t)) includescommon phase error, which is constant across the whole of thefrequencies, residual frequency offset (a linear phase component) andand time varying random phase contribution of local jitter. (Theresidual frequency offset is estimated separately, but can becompensated for together with the phase noise.) This process should beestimated, and its effect removed, since it introduces ICI. It isassumed that ψ(l) is a stationary process with a known covariancer_(ψ)(τ)=E[ψ(l)ψ*(l−τ)].

This assumption is very reasonable when the local oscillator is lockedto a stable frequency source through a phase-locked loop. ψ=(ψ₁, . . . ,ψ_(N))^(T) is defined to be a vector of N consecutive samples of thephase noise process ψ_(m)=ψ(mT_(s)). The covariance matrix of the phasenoise process is written as follows

$\begin{matrix}{R_{\psi\psi} = \begin{bmatrix}{E\left( {\psi_{1}\psi_{1}^{*}} \right)} & {E\left( {\psi_{1}\psi_{n}^{*}} \right)} \\{E\left( {\psi_{n}\psi_{1}^{*}} \right)} & {E\left( {\psi_{n}\psi_{n}^{*}} \right)}\end{bmatrix}} & (5)\end{matrix}$

R_(ψψ) can be decomposed using an eigendecomposition as

$\begin{matrix}{R_{\psi\psi} = {\sum\limits_{i = 0}^{N - 1}{\mu_{i}u_{i}u_{i}^{*}}}} & (6)\end{matrix}$

It is preferred to use the basis of the eigenvectors of R_(ψψ) forrepresenting the phase noise along a single OFDM symbol.

To explain the present invention in simpler terms, a single-inputsingle-output (SISO) model is described and then extended to amultiple-input multiple-output (MIMO) model. This generalization can bemade due to the fact that the phase noise is identical on all spatialchannels. It is assumed that the OFDM symbols are synchronized and thecyclic prefix has been removed, so that the channel matrix is circulantand is given by

$\begin{matrix}{H = \begin{bmatrix}h_{0} & h_{1} & \ldots & \ldots & h_{L} \\h_{L} & h_{0} & ⋰ & \; & h_{L - 1} \\\vdots & ⋰ & ⋰ & ⋰ & \vdots \\\vdots & \; & ⋰ & ⋰ & \vdots \\h_{1} & \ldots & \ldots & h_{L} & h_{0}\end{bmatrix}} & (7)\end{matrix}$

Furthermore, a single OFDM symbol will be considered.

The time domain OFDM symbol defined in (1) can be written in terms ofdiscreet Fourier transform (DFT) asx=F*s  (8)

wheres=[s₀, . . . , s_(N-1)]^(T)  (9)

is the frequency domain OFDM symbol.

The received OFDM symbol after removal of the cyclic prefix z=[z₀, . . ., z_(N-1)]^(T) is nowz=e ^(jΦ) Hx+n  (10)

where n=[n₀, . . . , n_(N-1)] is the additive white Gaussian noise andΦ=diag (φ₀, . . . , φ_(N-1))  (11)

is a diagonal matrix containing the components of the phase noise vectoron the diagonal.

Define a received data matrix Z as follows

$\begin{matrix}{Z = {{{diag}(z)} = {\begin{bmatrix}z_{0} & \; & \; \\\; & ⋰ & \; \\\; & \; & z_{N - 1}\end{bmatrix} = {{Y\;{\mathbb{e}}^{j\;\Phi}} + N}}}} & (12) \\{where} & \; \\{y = {{Hx} + n}} & (13) \\{and} & \; \\{Y = {\begin{bmatrix}y_{0} & \; & \; \\\; & ⋰ & \; \\\; & \; & y_{N - 1}\end{bmatrix} = {{diag}({Hx})}}} & (14)\end{matrix}$

is the received signal when no phase noise is present. Thus, the task ofICI suppression is reduced to estimating the phase noise andconstructing a time domain vector that cancels the harmful effect of thephase noise.

Time domain compensation in SISO systems is now described.

The point of a time domain method for reducing the phase noise lies inusing available pilot data in order to estimate coefficients of arepresentation of the phase noise. First, the phase compensationalgorithm of Casas et al, is explained. Then, the choice of a basis forthe phase noise compensation is formulated. It will be shown that usinga fixed basis such as Fourier vectors or discrete cosine transformvectors does not provide large gains in terms of ICI cancellation. Next,a system-dependent and time-dependent basis is selected according to thereceived data. This constitutes the essential improvement of the presentinvention. This is important for ICI cancellation since the number ofavailable pilots is small and therefore only a few coefficients can beestimated.

We note that common phase noise removal is achieved by choosing thefirst basis vector to be the N dimensional all-ones vector 1_(N)=[l, . .. , l]^(T).

Let v₀, . . . , v_(N-1) be a basis for □^(N). Denote the phase noiserealization e^(jφ)=[e^(jφ1,), . . . , e^(jφ) ^(N-1) ]^(T) and let γ=[γ₀,. . . , γ_(N-1)]^(T) satisfy

$\begin{matrix}{{\mathbb{e}}^{{- j}\;\varphi} = {\sum\limits_{k = 0}^{N - 1}{\gamma_{k}{v_{k}.}}}} & (15) \\{Equivalently} & \; \\{{\mathbb{e}}^{{- j}\;\varphi} = {V\;\gamma}} & (16) \\{{{where}\mspace{14mu} V} = {\left\lbrack {v_{0},\ldots\mspace{11mu},v_{N - 1}} \right\rbrack.}} & \;\end{matrix}$

If one allows only d basis vectors V^((d))=[v₀, . . . , v_(d-1)] thecurrent problem could be presented as a least squares (LS) problem.{circumflex over (γ)} is to be found such that V^((d))γ cancels thephase noise optimally (in the LS sense), i.e.,

$\begin{matrix}{\hat{\gamma} = {\arg\mspace{11mu}{\min\limits_{\gamma}{{{\mathbb{e}}^{{- j}\;\varphi} - {V^{(d)}\gamma}}}^{2}}}} & (17)\end{matrix}$

Since the phase noise is not known, it should be calculated from knownOFDM pilot tones. In this case (17) is to be modified assuming that onehas known values s_(pilot)=[s_(i) ₁ , . . . s_(i) _(r) ]^(T). Let ŷ bean estimate of the time domain symbol with the phase noise removed:ŷ=ZV ^((d)) {circumflex over (γ)}□Hx+n  (18)

Since H is diagonalized by the DFT matrix F_(N), i.e., H=F_(N)ΛF*_(N),one obtains thatŝ=Λ⁻¹F_(N)ZV^((d)){circumflex over (γ)}  (19)

is an estimate of the received OFDM frequency domain symbol. DefiningW=Λ⁻¹F_(n)ZV^((d))  (20)

one obtains that the LS estimate of γ is given by

$\begin{matrix}{\hat{\gamma} = {\arg\mspace{14mu}{\min\limits_{\gamma}{{s - {W\;\gamma}}}^{2}}}} & (21)\end{matrix}$

Therefore{circumflex over (γ)}=W_(pilot) ^(†)s_(pilot)  (22)

where s_(pilot) is obtained by choosing the rows that correspond topilot tones only.

The estimate of the phase noise cancellation vector is now given bye^(−jφ)=V{circumflex over (γ)}  (23)

It should be noted that the components of Z are affected by noise andthe noise is multiplied by Λ⁻¹. This implies that the estimation of γcan be improved using weighted LS (WLS) and total least squares (TLS)instead of the LS method described above.

At this point, the choice of basis vectors v₀, . . . , v_(N-1) is to bedetermined. The Casas method suggests the use of either the columns ofthe DFT matrix F_(N) or the columns of the Discrete Cosine Transform(DCT) matrix. This assumption has been tested in simulations and onmeasured phase noise and it was shown that this choice typically leadsto a minor improvement over canceling the common phase only, which meansthat ICI is still significant. In the present invention it is proposedthat a different approach should be applied, choosing the basis elementsusing the statistical properties of the phase noise process. For thispurpose, the phase covariance can be represented as

$\begin{matrix}{R_{\psi\psi} = {\sum\limits_{k = 0}^{N - 1}{\mu_{k}u_{k}u_{k}^{*}}}} & (24)\end{matrix}$

where u₀, . . . , u_(N-1) are the eigenvectors corresponding toeigenvalues μ₀> . . . >μ_(N-1) respectively. This basis is the bestchoice for representing random realizations of a random process withcovariance R_(ψψ) (this is a KL representation of the process). Becausethe statistical properties of the phase noise process are stationary forquite a long period of time, they can be calibrated in advance.

Another enhancement of the present invention is the use of aprediction/smoothing mechanism. The coefficients {circumflex over(γ)}_(i) can be tracked independently (FIG. 5), in this case for each ithe previous values of {circumflex over (γ)}_(i) are fed into a filterwith coefficients β_(i1), . . . , β_(iL), then {circumflex over (γ)}_(i)are smoothed on the basis of β_(i1), . . . , β_(iL). Alternatively, ajoint tracking of {circumflex over (γ)}₁, . . . , {circumflex over(γ)}_(d) using a matrix finite impulse response (FIR) filter can beperformed. This tracking is done using a multidimensional recursiveleast square (RLS) solution. In this case the previous values of{circumflex over (γ)}₁, . . . , {circumflex over (γ)}_(d) are fed into amatrix FIR system that is adapted based on previous decisions (FIG. 6).

The algorithm proposed in the present invention ensures reasonablecomputer running time. The complexity of the phase noise reductionprocess is estimated as follows.

The compensation of the phase noise involves dN complex multiplicationswhere d is the number of the basis elements. This is less than the fastFourier transform (FFT) complexity adding d multiplications per symbol.The main complexity is hidden in the LS itself. However, it should benoted that forming the matrix W involves computingW=Λ⁻¹F_(N)ZV^((d))  (25)

However, Λ⁻¹F_(N)Z is a diagonal matrix composed of the frequency domainequalized, which receives symbols that are generated withoutcompensating for the phase noise effect. Solving the LS problem (21)involves only matrices of size n_(pilot)×d resulting in cn_(pilot)d²operations. The power-like complexity enables an efficientimplementation of the novel method presented in this invention in realsystems.

Reference is now made to the accompanying figures, which illustrateaspects of the present invention as described above.

FIG. 1 illustrates a method of phase noise coefficient estimation. Thephase noise can be decomposed in some basis v₀, . . . , v_(N-1) withcoefficients γ=[γ₀, . . . , γ_(N-1)]^(T) (eq. 15). To estimate the{circumflex over (γ)}, pilot and null tones are used as an input (eq.18-20). {circumflex over (γ)} are calculated by a least squares (LS)procedure. The evaluation of {circumflex over (γ)} can be furtherimproved using weighted LS (WLS) and/or total LS instead of LS.

FIG. 2 shows schematically the phase noise compensation process (eq.7-14). The coefficients {circumflex over (γ)} and basis vectors v₀, . .. , v_(d-1) of the phase noise decomposition are multiplied respectivelyand then summed over (Σ) to get e^(−j{circumflex over (φ)}) ^(i) . Themultiplicative noise e^(−j{circumflex over (φ)}) ^(i) is then removedfrom received OFDM signal z_(i). The resulting signal y_(i) with nophase noise present is finally FFT transformed and processed byfrequency domain equalizers (FEQ).

FIG. 3 depicts calibration-based basis estimation. In the prior art(Casas) the constant basis of eigenvectors of DFT or DCT is usedindependent of the statistical properties of the phase noise. This doesnot provide a desirable degree of phase noise elimination. The presentinvention suggests a choice of the basis elements from the statisticalproperties of the phase noise itself. It is assumed that the phase noisehas covariance R_(ψψ) with eigenvectors u₀, . . . , u_(N-1)corresponding to eigenvalues μ₀> . . . >μ_(n-1). Samples of the phasenoise are generated and used to estimate R_(ψψ). Alternatively R_(ψψ)can be computed from the specific design of the local oscillator and thephase locked loop (PLL) regulating it. The proper basis v₀, . . . ,v_(N-1) should be now chosen from the singular value decomposition(which is equivalent to the eigenvalues) of R_(ψψ).

It is claimed by the present invention that the eigenvectors u₀, . . . ,u_(N-1) are the best choice for the basis v₀, . . . , v_(N-1) of themultiplicative phase noise expansion (eq. 24). Furthermore, if thechoice is limited only to d (for any d<N) vectors then the best choiceis to select u₀, . . . , u_(d-1).

In FIG. 4, a decision-directed basis estimation is presented. Thisenhances the proposed method of FIG. 3 by allowing the basis itself toadapt to environmental changes. Based on the previous symbol estimation,the W matrix is updated (eq. 20). Then using the LS or WLS procedure,one finds eigenvalues of the multiplicative phase noise expansion (eq.21-23) and the phase noise covariance R_(ψψ) is updated. Finally, fromthe covariance matrix one extracts the updated basis v₀, . . . , v_(N-1)for the phase noise expansion. The updates can be used for direct updateof the dominant subspace using subspace tracking techniques, such as theprojective approximation subspace tracking algorithm [Yang] or similartechniques.

FIG. 5 illustrates an independent tracking of coefficients {circumflexover (γ)} of the multiplicative phase noise expansione^(−j{circumflex over (φ)}) ^(i) . For each i the previous values of{circumflex over (γ)}_(i) are fed into a filter with coefficientsβ_(i1), . . . , β_(iL), then {circumflex over (γ)}_(i) is smoothed onthe basis of coefficients β_(i1), . . . , β_(iL).

FIG. 6 shows schematically joint tracking of coefficients γ=[γ₀, . . . ,γ_(N-1)]^(T) with the use of a finite impulse response filter (FIR).Previous values of {circumflex over (γ)}₁, . . . , {circumflex over(γ)}_(d) are fed into a matrix FIR system that is adapted based onprevious decisions, and then the tracking is done using amultidimensional RLS solution.

FIGS. 7 to 18 present experimental results from a simulation of thetechnique for phase noise reduction disclosed in the present invention.The simulation tested the technique's performance on measured WLANchannels and using measured phase noise.

The channels are depicted in FIG. 7. The transmitted power was 13 dBmand the assumed noise figure was 7 dB. The phase noise was generatedusing a third order Chebychev type I filter with cut-off frequency of150 kHz and PSD depicted in FIG. 8.

The standard deviation of the phase noise was 3°. Two channels and tonesnumber 1-7, 21, 43, 58-64 at each of the two receivers were used. FIG. 9presents a constellation diagram based on 100 OFDM symbols and 64 tones.Note the 0 symbols in the center of the diagram. The large performanceenhancement is clearly visible. FIG. 10 presents the results of the sameexperiment using DFT basis vectors as suggested by Casas. The differencein performance is clearly visible. FIG. 11 depicts the dependence of theresidual error vector magnitude (EVM) on the number of basis elementsusing Karhunen-Loeve (KL) basis vectors and discreet Fourier transform(DFT) basis vectors. The KL eigenvectors were computed based on 3 OFDMsymbols. For a large number of parameters the EVM is larger due to theinsufficient number of equations. The large gain compared to the DFTbasis is clearly visible. To obtain the performance under good phasenoise and channel conditions, the experiment was repeated with phasenoise of 0.7° and with the channels attenuation reduced by 5 dB comparedto FIG. 7. The results are presented in FIG. 12 to FIG. 15. Even in thiscase, there is a substantial gain by canceling the phase noise, althoughthe phase noise performance is reasonable even with CPE-onlycompensation.

In the second set of simulated experiments, phase noise samples weremeasured. The measured signal included a sine wave at 5 MHz, sampled at40 MHz and then filtered to remove the sine wave. The PSD of the phasenoise is depicted in FIG. 16. This experiment was repeated with samplesof the measured phase noise. The results are depicted in FIG. 17. Thegain is lower, but it is still substantial.

FIG. 18 depicts the structure of a basic SISO receiver as suggestedaccording to the present invention. The SISO receiver is a conventionalOFDM receiver known in the prior art (van Nee and Prasad) with a newunit 106 added for performing the phase noise compensation. Unit 101 isthe radio frequency (RF) frontend connected to the antenna andperforming down conversion of the received RF signal into a basebandsignal. The baseband signal is sampled using an analog-to-digitalconverter (unit 102). The baseband receiver removes the cyclic prefix(unit 103) and converts the input stream into synchronized blocks of Nsamples (unit 104). The data is then directed into the phase noiseestimation unit (106), which provides a phase noise compensating signal(Equation 23). In parallel the original data is buffered through unit(105) and then multiplied by the respective sample of noise compensatingsignal (Equation 23) and transferred to a Fast Fourier Transform (FFT)unit (107). The output of the FFT is then processed in a frequencydomain processing unit 108, which performs frequency domainequalization, soft demapping, deinterleaving, and decoding of theforward error correction code etc.

FIG. 19 illustrates the phase noise estimation unit 106 shown in FIG.18. Unit 106 consists of FFT unit 201, which computes the receivedsignal using the pilot tones and null tones. FFT unit 201 can bereplaced in some cases by a Direct Fourier Transform (DFT) unit becausethe number of pilot tones is small compared to the FFT size, or by othertypes of units which are based on other known in the art techniques forextracting the pilot and null tones. The received tones are then fedinto coefficient estimation unit 202 (detailed in FIG. 1), whichestimates basis coefficients of the phase noise. The estimatedcoefficients are then fed into compensating signal generation unit 203(detailed in FIG. 2), which uses the system and time-dependentrepresentation and the coefficients to generate phase noise compensatingsignal.

While the above description contains many specifics, these should not beconstrued as limitations on the scope of the invention, but rather asexemplifications of the preferred embodiments. Those skilled in the artwill envision other possible variations that are within the scope of theinvention. Accordingly, the scope of the invention should be determinednot by the embodiment illustrated, but by the appended claims and theirlegal equivalents.

1. A method of reducing phase noise in OFDM systems the methodcomprising: obtaining a received data matrix Z that is diagonal andexhibits sampled OFDM signal values z in accordance with a received OFDMsignal comprising transmitted OFDM signal multiplied by a known phasenoise process over a channel having a matrix channel H, wherein the OFDMsignal comprises at least one pilot tone; obtaining a covariance matrixof the known phase noise process; decomposing the covariance matrix intoeigenvectors; creating a matrix V from all decomposed eigenvectors;calculating a discrete fourier transform matrix F representing thetransformation from an OFDM symbol to OFDM signal in a particular OFDMsystem; diagonalizing the channel matrix H utilizing Matrix F;calculating a matrix W by multiplying an inverse matrix of thediagonalized H matrix, with matrix F, matrix Z, and matrix V; estimatingthe phase noise coefficients by multiplying W with the at least one OFDMpilot tone; and estimating a phase noise cancellation vector bymultiplying the estimated phase noise coefficients with matrix V.